(3) Find the formula for the number of ways for putting n identical balls into k distinct boxes so that none of the boxes gets more than r boxes. What happens if the boxes are also identical?

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A: N is the set of natural numbers, so it start from 1.

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Q: Evaluate S. So dy 0 dx √√[y(1+x²)]

A: Problem is solved using concept of integral.

Q: (B): Find the integration by using substitution method fx √2x - 1 dx

A: here we use basic integral form

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Q: Ⓒ 22 it M = {1, 2, 3, 4, 5, 6,7,8} and of is given in the Table: 1 2 3 4 5 6 7 8 I 2 6 1 3 8 457 1)…

A: Given: The set, M=1,2,3,4,5,6,7,8 and the permutation, M  1  2  3  4  5  6  7  8F   2  6  1  3  8  4…

Q: Find the formula for the number of ways for putting n identical balls into k distinct boxes so that…

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Q: Find the y(t)

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Q: (b) compute an estimate of x(2) for the initial-value problem dx 1 x(1)=2 dt x+t using step size h =…

A: Problem is solved using concept of fourth-order runge-kutta method.

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Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: We can solve this using given information

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A: This is a problem of Logic.

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Q: 5. The dimensions of a cylindrical object are increased by a scale factor of 3. The volume of the…

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Q: (B) Use Tabular integration f(t³-4t² to evaluate the following: - + 5t+32) sin(t)dt

A: we have to evaluate given integral by tabluar method ∫(t3-4t2+5t+32)sin(t)dt

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Q: 4.1. Derive the heat equation with a metal rod with variable cross-sectional area A(x). Using the…

A: We have to drive the heat equation with a metal rod with variable cross-sectional area.

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A: Since  you have posted a multiple  question according to guildlines I will solve first   question…

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Q: (c) (i) Find all the square roots of 1 in Z25 and Z32. Find all the square roots of 9 in Z800- (ii)…

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Q: How many positive integers divide 10!. 3 C =

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A: Given that function f(x)=x+1      x&gt;2x2-1    x≤2To check Differentiability We find Left hand…

Q: (III) Find the Half-range Sine series of f(x) = sin(x) on (0,2).

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Q: our work on additional pieces of paper. (1) Consider the system of equations x- 2y + 3z = 9 -x+3y-z…

A: given system of equations x-2y+3z=9-x+3y-z=-62x-5y+5z=17 According to the guidelines I am answering…

Q: a) How many derangements ) How many derangements has the set S? of S have 9 in the 2nd position and…

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Q: Hand written plzz how? please explain step by step 6. Assume that there are only three possible…

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Q: Determine the antiderivatives of the following functions: 1. f(x + 1)100 dx 2. f(x² + x)¹0 (2x +…

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